The effect of temperature oscillations at the growth interface on crystal perfection

Kuroda, Ekyo; Kozuka, Hirotsugu; Takáno, Yukio

doi:10.1016/0022-0248(84)90468-8

Cited by 37 publications

(3 citation statements)

References 18 publications

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“…The temperature gradients in the crystal and melt have been measured directly. [8][9][10][11][12][13] Although the correlation between G s and V is positive in Refs. 4-6, 14, 15, the negative correlation between G s and V is reported, 11,16) which is against with the simplified conservation of energy at the interface.…”

Section: Introductionmentioning

confidence: 99%

Effect of density change at crystallization on a one-dimensional heat balance equation at solid–liquid interface

Mori

Sato

Suzuki

2019

Jpn. J. Appl. Phys.

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In this paper, we study how we should treat a steady-state interface between homogeneous crystal and melt phases, where steady temperature gradients are present at both sides. In particular, keeping the geometry of Czochralski method in mind, we study a correction for the heat balance equation at the interface between the two phases. We show that a netagive term proportional to the third power of the pulling velocity, which is caused by the density difference between the two phases, is added to the heat balance equation.

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Section: Introductionmentioning

confidence: 99%

Effect of density change at crystallization on a one-dimensional heat balance equation at solid–liquid interface

Mori

Sato

Suzuki

2019

Jpn. J. Appl. Phys.

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“…The first benefit of a magnetic field is the elimination of turbulence and all large-scale periodicity in the melt motion (Hirata & Hoshikawa 1992). Temporal fluctuations in the heat transfer and oxygen or dopant transport from the melt to the growing crystal produce many microscopic structural defects and microscopic concentration variations in the crystal (Kuroda, Kozuka & Takano 1984). Recent advances in integrated-circuit manufacturing have dramatically increased the number of transistors per cm2 of wafer surface and have led to the need to eliminate microscopic defects and concentration variations in the CZ crystals from which the wafers are sliced.…”

Section: Introductionmentioning

confidence: 99%

Thermocapillary convection in a cylinder with a strong non-uniform axisymmetric magnetic field

Khine

Walker

1994

J. Fluid Mech.

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This paper treats a surface-tension-driven liquid-metal flow in a cylinder with a steady externally applied non-uniform axisymmetric magnetic field. The top boundary consists of an annular free surface around a solid disk, modelling the Czochralski growth of silicon crystals. A radial temperature gradient produces a decrease of the surface tension from the disk edge to the vertical cylinder wall. The magnetic flux density is sufficiently large that inertial effects and convective heat transfer are negligible. First we present large-Hartmann-number asymptotic solutions for magnetic fields with either a non-zero or a zero axial component at the free surface. The asymptotic solutions indicate that a purely radial magnetic field at the free surface represents a singular limit of more general magnetic fields. Secondly we present numerical solutions for arbitrary values of the Hartmann number, and we treat the evolution of the thermocapillary convection as the axial magnetic field at the free surface is changed continuously from the full field strength to zero.

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“…The magnetic field suppresses turbulence in the melt and the associated fluctuations in the heat flux across the crystal-melt interface. Because of these fluctuations, without a magnetic field the crystal alternately grows and remelts, which produces more microdefects in the crystal (Kuroda, Kozuka & Takano 1984). A crystal grown in a magnetic Czochralski puller has a lower microdefect density.…”

Section: Introductionmentioning

confidence: 99%

Melt motion in a Czochralski crystal puller with an axial magnetic field: motion due to buoyancy and thermocapillarity

Hjellming

Walker

1987

J. Fluid Mech.

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In the Czochralski process a single crystal is grown from liquid in a crucible. An axial magnetic field suppresses turbulence in the melt and thus reduces the density of microdefects in the crystal. This paper treats the melt motion due to buoyancy and thermocapillarity. The magnitude of this motion decreases roughly like B−2, as the magnetic field strength B is increased. The separate circulations due to buoyancy and thermocapillarity are roughly equal at an early stage of growing a crystal. However the circulation due to thermocapillarity is nearly independent of the melt depth, while that due to buoyancy is proportional to the square of the depth. Therefore as the crystal grows and the melt depth decreases, thermocapillarity becomes progressively more dominant. When the heat flux into the melt is used to define the characteristic temperature difference and velocity, the stream functions are rather insensitive to changes in the thermal boundary conditions at the free surface and at the crucible bottom, provided the overall heat balance of the system is correctly estimated. This is fortunate because there is considerable uncertainty about these boundary conditions. The exception to this insensitivity is that the melt motion due to thermocapillarity is sensitive to changes in the amount of heat lost through the part of the free surface adjacent to the crystal.

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The effect of temperature oscillations at the growth interface on crystal perfection

Cited by 37 publications

References 18 publications

Effect of density change at crystallization on a one-dimensional heat balance equation at solid–liquid interface

Effect of density change at crystallization on a one-dimensional heat balance equation at solid–liquid interface

Thermocapillary convection in a cylinder with a strong non-uniform axisymmetric magnetic field

Melt motion in a Czochralski crystal puller with an axial magnetic field: motion due to buoyancy and thermocapillarity

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